Question

In a​ poll, 51​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" The margin of error in the poll was 2​%, and the estimate was made with 96​% confidence. At least how many people were​ surveyed?

Answer 1

Solution :

Given that,

= 0.51

1 - = 1 - 0.51 = 0.49

margin of error = E = 2% = 0.02

At 96% confidence level the z is,

= 1 - 96%

= 1 - 0.96 = 0.04

/2 = 0.02

Z/2 = 2.05    ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.05 / 0.02)2 * 0.51 * 0.49

=2626

Sample size = 2626